\chapter{Literature summary}
This chapter is a for the most part a summary of the more extensive litterature review done in the project, \emph{\textit{Irreversibility of combustion, heat and mass transfer}} \cite{PedramProject}. 

\section{Papers}
Dunbar and Lior \cite{Dunbar1994} where possibly the first to investigate the details of the sources of combustion irreversibility. . Their method was a simplified approach which did not require solving the spatial Navier-Stokes, energy and reaction kinetics equations, but instead they divided the entire combustion phenomenon into four hypothetical sub-processes and applied them along prescribed process paths. Through careful reasoning they evaluated the irreversibility using a finite increment exergy analysis method. The analysis was performed for combustion of CH4 and H2. Their proposed process paths where:
\begin{enumerate}
	\item a diffusion process where the fuel and oxygen molecules are drawn together
	\item	a chemical reaction process leading to oxidation of the fuel
	\item	an internal heat transfer between high temperature product and the unburned reactant
	\item	a physical mixing process where the system constituents mix uniformly
\end{enumerate}
Out of the total exergy destruction, 72-77\% was caused by internal heat exchange, 15-18 \% due to chemical oxidation reaction and 8-10\% due to gas mixing. The analysis of Dunbar and Lior was able to provide important results with a hypothetical approach which did not involev physical models.


Ertesvåg and Kolbu \cite{Ertesvåg2005} used the CFD code SPIDER with EDC (Eddy Dissipation concept) for turbulent combustion under a fast chemistry assumption. They separated the entropy production into its mean and turbulent parts. For the mean entropy production rate they found the heat flux contribution to be the dominating source of irreversibility. The major production of entropy happened in the fine structure, which represents the smallest eddies in the turbulence . The reason for this is that in the EDC the vast majority of chemical reaction happens in the fine structure.

Som, Agrawal and Chakraborty (2007) \cite{Som2007} studied the irreversibilities in an impinging flame. They noted that the dominant source of thermodynamic irreversibility in a diffusion flame is due to chemical reaction and that the irreversibility component of each physical process is higher for diffusion flames than for premixed flames.

Som, Mondal, Dash ~\cite{Som2005}. PDF mixture fraction approach is used. The standard k-$\epsilon$ model was used to model the turbulence despite it's shortcomings for modeling swirling flow. Increasing the inlet pressure form 100 kPa to 500 kPa increases the combustion efficiency, but decreases the second law efficiency. This effect is most drastic for zero-swirl condition. This is caused largely because unburnt particles in the exhaust increase the chemical exergy at the outlet.

Rakoupoulos and Michos ~\cite{Rakopoulos2009} look at the combustion of biogas-hydrogen mixtures in spark ignition engines. They find that increasing the amounts of hydrogen in biogas decreases the rate of irreversibility production in the flame. This can be attributed to the increase of combustion temperature with increased amounts of $H_2$ in the fuel.

Nishida and Takagagi (2002) \cite{Nishida2002} found chemical reaction to be the dominant source of combustion irreversibility in laminar flames. For a turbulent diffusion flame they found that the biggest contribution.

\cite{Stanciu2001} used the prescribed PDF method to quantify the sources of entropy production in a turbulent nonpremixed $CH_4$ flame. They divided the contributions to entropy generation in turbulent and laminar subrelations. They found that 98\% of the entropy production comes from the turbulent 